e r a question

[banny]

How do you figure a pitcher's ERA if he goes in, gives up 5 runs, gets no one out and is taken out? He doesn't ge any credit for innings pitched and if you divide er x 9 by ip, it's always zero.

[scorekeeper]

How do you figure a pitcher's ERA if he goes in, gives up 5 runs, gets no one out and is taken out? He doesn't ge any credit for innings pitched and if you divide er x 9 by ip, it's always zero.

The result for that calculation isn’t zero, its undefined. What I do when that happens, is have the computer replace the undefined answer with 99.99. Its all usually moot though, as soon as the pitcher gets even 1 out.

[leewileyfan]

I've seen it typed in as the infinity symbol.

[Iowanic]

Usually they just say he was pitching for the cubs at the time. It's all the info required...

[drstrangelove]

How do you figure a pitcher's ERA if he goes in, gives up 5 runs, gets no one out and is taken out? He doesn't ge any credit for innings pitched and if you divide er x 9 by ip, it's always zero.

Although you will often see it shown in baseball books as infinity, this I think is incorrect, and Scorekeeper said, should be denoted as undefined (undef). Infinity is for different mathematics. Simple real numbers should be undefined. It's never zero.

[WillMorrison]

I disagree, I think infinity is more accurate than undefined. An ERA answers the question "If this pitcher pitched 9 full innings, how many runs would he give up?" Since he would never get an out, he would give up an infinite number of runs.

The two sides of this argument are basically arguing the same thing, though: This pitcher just plain sucks, or at least on that day.

[Jackaroo Dave]

I disagree, I think infinity is more accurate than undefined. An ERA answers the question "If this pitcher pitched 9 full innings, how many runs would he give up?" Since he would never get an out, he would give up an infinite number of runs.

The two sides of this argument are basically arguing the same thing, though: This pitcher just plain sucks, or at least on that day.

The way you have phrased the question, "If this pitcher pitched 9 innings . . ." shows that the answer is "undefined," since the condition would never be met.

Mathematicians conventionally define division in terms of multiplication: A/B = C if and only if A = B*C.

So X/0 = infinity if and only if X = 0 * (infinity). But 0*(infinity) doesn't equal any number in particular.

If X/0 = infinity, then 1/0 = infinity and 2/0 = infinity, so 1 = 0*(infinity) = 2. So X/0 is undefined.

[NYYankeesFan92]

Does anyone else care to take a crack at this?

[Armster]

The way you have phrased the question, "If this pitcher pitched 9 innings . . ." shows that the answer is "undefined," since the condition would never be met.

Mathematicians conventionally define division in terms of multiplication: A/B = C if and only if A = B*C.

So X/0 = infinity if and only if X = 0 * (infinity). But 0*(infinity) doesn't equal any number in particular.

If X/0 = infinity, then 1/0 = infinity and 2/0 = infinity, so 1 = 0*(infinity) = 2. So X/0 is undefined.

This would be my answer, though the infinity response holds logic as well for a non-logical math problem that is.

[leewileyfan]

Does anyone else care to take a crack at this?

In computer language [IEEE floating point standard] division by zero is treated as +/- 0 or the infiinty symbol ... or NaN "not a number." The infinity symbol makes logical and linguistic sense to me in that our minds can readily cut to the chase, seeing anything divided by 0 being unlimited or endless. Conversely, multiply anything by zero and we can kind of figure out that it is annihilated, obliterated or rendered infinitely GONE.

I also like the Cub pitching staff reference.

[Jackaroo Dave]

Does anyone else care to take a crack at this?

I'm not anyone else, but I'll try to be clearer. "How do you figure the era of a pitcher who gives up 5 runs without retiring anybody?"

ERA = (earned runs)/(innings pitched)*9 = (5/0)*9. But in the real number system, division by zero is an undefined operation, so (5/0) does not mean or express anything. Consequently, (5/0)*9 doesn't mean anything either.

The short answer is, "You can't."

You can certainly say that the pitcher's ERA is infinity and be understood (though it would be fair to ask you, "Which infinity?"), but there is no way to calculate a mathematical solution.

[Jackaroo Dave]

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